Numerical computation of the spatial decaying wave characteristics for the design of locally resonant acoustic metamaterials

In structural dynamics, periodic resonant inclusions are widely used to improve the vibro-acoustic properties of lightweight structures. Depending on the design of these inclusions, the wave propagation in the structure is modified for specific frequency ranges and stop bands, where in theory no free wave propagation is possible, can be generated. The Wave Finite Element Method (WFEM) investigates the wave propagation in periodic structures based on a Finite Element (FE) model of a single unit cell. Using the direct approach of the WFEM, it is possible to depict the wave characteristics in the frequency range of the resonant frequency of the inclusions. Consequently, a spatial decay for the different wave types can be determined in the frequency range of the potential stop band. The frequency dependent decay characteristics can be used to evaluate the performance of the resonant inclusions and find optimal parameters for the desired application of the metamaterial. The procedure is applied to design beam-like resonators and find an optimal resonator spacing for a beam-like acoustic metamaterial. For a fixed percentage of added mass, the spacing of the resonators can be adjusted to optimize the maximum spatial decay or the stop band size.